Search results for "Continuous-time stochastic process"

showing 5 items of 15 documents

A new stochastic representation for the decay from a metastable state

2002

Abstract We show that a stochastic process on a complex plane can simulate decay from a metastable state. The simplest application of the method to a model in which the approach to equilibrium occurs through transitions over a potential barrier is discussed. The results are compared with direct numerical simulations of the stochastic differential equations describing system's evolution. We have found that the new method is much more efficient from computational point of view than the direct simulations.

Statistics and ProbabilityStochastic partial differential equationGeometric Brownian motionStochastic differential equationContinuous-time stochastic processQuantum stochastic calculusStochastic processLocal timeDiscrete-time stochastic processStatistical physicsCondensed Matter PhysicsMathematicsPhysica A: Statistical Mechanics and its Applications
researchProduct

Robust linear quadratic mean-field games in crowd-seeking social networks.

2013

We consider a social network where opinions evolve following a stochastic averaging process under the influence of adversarial disturbances. We provide a robust mean-field game model in the spirit of H∞-optimal control, establish existence of a mean-field equilibrium, and analyze its stochastic stability.

Stochastic controlContinuous-time stochastic processMathematical optimizationSocial networkStochastic processbusiness.industryControl (management)mean field gamesRobust controlStochastic neural networkbusinessGame theoryMathematical economicsMathematics
researchProduct

A Fokker–Planck control framework for multidimensional stochastic processes

2013

AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…

Stochastic controlMathematical optimizationContinuous-time stochastic processOptimization problemoptimal control stochastic processesStochastic processApplied MathematicsOptimal controlComputational MathematicsModel predictive controlMultidimensional stochastic processOptimal control theoryLimit cycleProbability density functionFokker–Planck equationFokker–Planck equationModel predictive controlMathematicsJournal of Computational and Applied Mathematics
researchProduct

Set-valued stochastic integral equations driven by martingales

2012

Abstract We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.

Stratonovich integralContinuous-time stochastic processApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISStochastic calculusRiemann–Stieltjes integralRiemann integralsymbols.namesakeQuantum stochastic calculusImproper integralsymbolsDaniell integralAnalysisMathematicsJournal of Mathematical Analysis and Applications
researchProduct

Stochastic model for complex surface-reaction systems with application toNH3formation

1993

A stochastic model is introduced that is appropriate to describe surface-reaction systems. These reaction systems are well suited for the description via master equations using their Markovian behavior. In this representation an infinite chain of master equations for the distribution functions of the state of the surface, of pairs of surface sites, etc., arises. This hierarchy is truncated by a superposition approximation. The resulting lattice equations are solved in a small region which contains all of the structure-sensitive aspects and can be connected to continuous functions which represent the behavior of the system for large distances from a reference point. In the present paper, we …

Superposition principleContinuous-time stochastic processDistribution functionStochastic modellingLattice (order)Monte Carlo methodMaster equationDynamic Monte Carlo methodStatistical physicsMathematicsPhysical Review E
researchProduct